Is it permissible to (i) take additional collateral (such as 2nd home or investment property) and (ii)have a provision by which the credit limit is automatically reduced because the additional collateral has been released?

You can do it, but you have to disclose it properly.

Program Disclosure Requirements

Under possible actions of the creditor, you will have to disclose that you can reduce the credit limit if collateral is partially released. This requirement can be found in 226.5b(d)(4). I do not believe that you have to specify the amount of the reduction, only state that the limit may be reduced, and either let the consumer ask for the list of reasons (sub-paragraph ii) or list the reasons (sub-paragraph iii).

Initial Disclosure Requirements

Same as above. See 226.6(e)(1).

Contract Requirements

The terms under which the limit will be reduced and the amount of the reduction should be spelled out in your contract. I would think you would want to be as precise as possible to prevent misunderstandings or issues later. That is a question for counsel, however.